Random Portfolio benchmarks

The growth of passive investing has a lot to do with investors migrating to lower-cost investment vehicles, but implicit in the migration to passive frameworks is a presumably lower risk metric. Investors want to be exposed to equities but don’t want to take risks beyond those inherent in the benchmark indexes they are investing in. Additionally, index investors are opting out of the risks of active management because the returns generated have recently not kept pace with the index benchmarks. But indexes are not what investors should be using as benchmarks. They don’t represent a truly passive approach to the market. The only truly passive approach to the markets is one that employs random portfolio construction.

Why random portfolios? Because all indexes are systematically biased by their factor premises. The prevalent index factor is size (market capitalization) but other factor frameworks include sector, industry, value, growth, momentum, and smart beta. Each of these index frameworks employs a systematic weighting of components based on a predetermined valuation that aims to minimize variability of returns based on defined factors.

Take a look at the S&P 500 index. It’s the most traded index in the world - through ETFs like SPY - but more importantly is the primary benchmark for U.S. equities. The performance S&P 500 index guides investors in terms of relative performance of actively managed funds and ultimately is the most broadly used compensation metric of the asset management industry. The fees investors pay these managers and, ultimately, the employment, compensation and rewards these fees fuel depend on the structure of the index.

The S&P 500 index is first and foremost a members club. Stocks are included in the index by decision of a committee. Yes, constituent stocks must meet certain primary criteria - market capitalization (float-adjusted weightings), liquidity, domicile, public float, sector classification, financial viability, and length of time publicly traded and stock exchange - but the criteria is set by a member board. And it’s set with a certain purpose in mind: the index is a gauge of large cap U.S. equities.

So we know that the SPX is a factor-based measure of U.S. equities - it tells us about the price movement of large-cap stocks. That should surprise few people. Implicit in this size factor is the fact that the SPX accounts for about 80% of the entire capitalization of the U.S. stock market. That’s a good chunk of the assets invested in this market.

However, the size factor weighting of the SPX is problematic when it comes to fulfilling the index’s role as a benchmark. The size bias distorts the benchmark performance and concentrates on the largest companies, often adding additional risk in those constituents because many are in the same sector or industry. In fact, the current weighting of the SPX shows that about 28% of the index weighting is in technology stocks. Further, the top 4 stocks by weight in the index are Apple, Microsoft, Amazon, and Facebook. The S&P 500 index has a decidedly tech bias at this time, a considerable sector risk for a benchmark index that is ostensibly supposed to track the overall performance of U.S. equities.

That may be a reasonably correct weighting of big cap U.S. equities, however, it’s not a correct benchmark measure of alpha. Alpha is the intelligence that extracts investment returns above the market performance. A portfolio of stocks constructed with a size bias only tells us about the performance of the bias. It does not represent the performance of a naive portfolio - a portfolio of stocks that has no factor bias. A naive portfolio would not have a selection criteria that restricts to a subset of a given universe of stocks. It would be a portfolio derived from a set of randomly selected stocks.

Random portfolio returns give us an estimate of the returns that are built into the broad market. Irrespective of factors that deliver alpha, a measure of random portfolio returns tells us the returns a given market generates without having any specific intelligence about how to generate those returns. They are the returns that would be generated by an untrained monkey.

What have been the random portfolio returns of the U.S. equity market? How do they compare to the returns of the S&P 500 index? Below is an annual comparison of 52-week returns (%) of the market cap index and the mean (average) return (%) of randomly selected portfolios. The last column shows the differences in returns (%) between the market cap index (SPX) and the random portfolios.

The random portfolio returns are the mean return (%) of 1,000 randomly selected portfolios of 100 common stocks selected at the beginning of the return period. That would be equivalent to 1,000 different monkeys picking a 100 stock portfolio, then taking the average return of those 1,000 portfolios after the 52-week period. The universe of stocks from which these random portfolios are selected includes all NYSE/Nasdaq listed common stocks that have traded for at least 40-weeks trading at a price above $2 and weekly trading volume above 100,000 shares. That would be a universe of about 3,900 stocks.

Annual returns (%) - SPX and random portfolios

This summary tells us that the S&P 500 index has only out-performed the random portfolios in 7 of the last 15 years (2003-2017) and that the sum of the differences in return is -26.3%. The monkey would have outperformed the S&P 500 index over the period by a significant amount. However, we can also see that much of this outperformance comes in 2003 and 2009, both years where the overall market enjoyed exceptional returns after a bear market. Clearly, those were periods where the size bias of the S&P 500 index excluded it from returns that were delivered elsewhere in the market (small-cap stocks, growth stocks, momentum stocks, etc.).

Presently, the S&P 500 index is providing excess returns above the benchmark represented by random portfolios. On the surface that tells us that portfolios weighted toward large-cap - specifically large-cap technology stocks - are outperforming the market. They will until they don’t. Investors should be aware of where their returns are coming from and where their risk is situated. The S&P 500 index is not a passive index. It is not market agnostic.

Stock Trends Slots game!

There is a new Stock Trends learning application installed on the Stock Trends website - a slots game! The Stock Trends Slots game engages users by generating random sets of stocks and matching combinations of their Stock Trends indicators. These matching combinations score points based on the probabilities of the match. Every week a new set of Stock Trends indicators reflect the changing stock market, so the game’s probabilities and rewards change with the distribution of the indicators.

Investors might wonder how a random outcome game applies to the markets. But there are aspects of skill in the game that come with the premium functions subscribers to Stock Trends Weekly Reporter may access. The ability to lock game rows allows users to improve the probabilities of making a match without a corresponding reduction in reward. That means a skillful player who understands the distribution of trend and price momentum indicators in a current market can achieve higher scores.

Each spin of the game creates a random portfolio of five (5) stocks and/or ETFs. This is a useful application of random portfolio generation that also makes for an interesting stock market game. These random portfolios - generated by the Stock Trends Slots game play - can be entered into the Stock Trends Investor Challenge, a weekly stock market competition to see which portfolio has the best return after 4-weeks of actual market activity.

This stock market game helps illustrate how random portfolios perform relative to the market benchmarks. Users have some degree of skills-based intervention in the Stock Trends Investor Challenge as they can either choose to enter their slots game portfolio, or not. The Stock Trends indicators help give guidance on that decision, just as they do for actual stock market analysis.

Give it a try!

Stock Trends Slots

Trend profile - SPDR S&P Metals & Mining ETF $XME

Stock prices tend to move in trending patterns. This is a simple idea that may, or may not be supported by evidence. It really depends on how you frame the question and what time frame is presented. That’s because prices also tend to revert to a mean or average price. This interplay of price trend and price reversion is a fundamental dynamic of the market. It’s also the window dressing for evidence of randomness that underpins market price patterns.

It’s easy to not recognize randomness when we focus so much on trend and reversion. A core mechanism for human understanding is our ability to identify patterns and formulate responses to them. Indeed, much of our learning is dependent upon pattern recognition. Why shouldn’t our understanding of the markets be based on the same formulations?

Many successful trading strategies are based on pattern recognition. Whether fundamental or technical in nature, these systems win when the precepts of their approach match what the market is delivering at any particular span of time. Market is trending: systems based on price trend patterns win. Market is reverting: systems based on price reversion patterns win. A truly intelligent trading system would know how to recognize the difference between the two and when to apply either a price trend system or a price reversion system. (Orpheus Risk Management Indices (RMI) is one such intelligent system http://www.orpheusindices.com/)

However, attempts to predict outcomes in a world of true randomness cannot be absolutely defended, by definition, no matter how intelligent. Looking for patterns in randomness brings us to Chaos theory and fractal mathematics, which explores the transitions between order and disorder in deterministic systems dependent of initial conditions.

This is heady and fascinating stuff that has a growing influence on financial markets analysis, but how does a stockpicker fit in all this? It’s no wonder that the era of the stockpicker is quickly transforming into algorithmic and machine learning systems increasingly favoured by capital markets money managers. That’s all well and good for highly capitalized institutional shops, but what about the little guy?

The Stock Trends Inference Model (STIM) is an attempt to reconcile randomness in the market with evidence of price patterns. It is a simple application of statistics to Stock Trends categorical indicators that answers some basic questions about certain trend characteristics. Examples of these questions include: If the price momentum of a stock is relatively high and it has been in a bullish trend for a relatively long period, will the price momentum continue, and for how long? If a price trend has changed from bearish to bullish, what are expectations for price momentum going forward? If a stock breaks out of a bearish trend, what are the probabilities it will it retreat?

All of these questions are asked with the assumption that the answers provided are independent of the present broad market condition. That is, we want to know return expectations regardless of whether the market is in a bull or bear trend. Why? Because we cannot know whether the present trend of the market will persist. If we make an assumption that it will, then our measurement of the expected returns of an individual market (stock, ETF) will be imprecise.

This is important. When we take a measurement of a particular market condition - as represented in the combination of Stock Trends indicators in each weekly Stock Trends Report for individual stocks and ETFs - the observations of similar market conditions will take place across time periods that span the entire population of observations. Each observation occurs in varying broad market trend phases. In this respect, the Stock Trends Inference Model is broad market agnostic.

For that reason, the base measurement of returns is relative to the historical random returns of stocks, which is about 8% annually, and specifically equate to the following expected returns for each of the relevant periods Stock Trends measures: 0% 4-week return, 2.19% 13-week return, and a 6.45% 40-week return. If a trend condition for a particular stock/ETF does not provide statistical evidence that it can beat these base return expectations, then we cannot say anything definitive about its return expectations. However, if there is a deviation from the base return expectations we can say that the current trend characteristics indicate either over-performance or under-performance projections. This is the objective of the Stock Trends Inference Model.

A good starting point for Stock Trends Weekly Reporter subscribers is a weekly review of the STIM Select stocks report. It shows the stocks and ETFs that have the best statistical trend characteristics. The report is ranked by the 13-week return expectations.

The current NYSE STIM Select report, as an example, includes the SPDR S&P Metals & Mining ETF (XME-N).  The Stock Trends Report for XME shows that the ETF is 7-weeks into a Weak Bullish trend; that it is underperforming the S&P 500 index by 12% over the past 13-weeks and underperformed the broad market index last week  (RSI 88 - ). It’s been in a Bullish category for 54-weeks but has been retreating since February.

The statistical model shows that there have been about 277 observations of stocks and ETFs that have shared these characteristics or have had similar Stock Trends indicator combinations. From this sample we can make inferences about the expected returns of XME over the next 4-week, 13-week, and 40-week periods.

The green sample density plots show the distribution of returns for the three separate periods following the observation. Most generally, these distributions will be centered around the mean random return expected for each period ( 0% 4-week return, 2.19% 13-week return, 6.45% 40-week return). However, certain Stock Trends indicator combinations yield sample distributions that deviate from the expected mean random returns. The sample distribution of returns generated in the XME sample deviate in a positive way.

For the 4-week period 53.8% of returns in the sample are greater than 0%, the expected 4-week return. By employing statistical inference methods to estimate the population mean, we can estimate that the expected (or mean) 4-week return for XME is 1.8%. More importantly, with our assumption of a normal distribution of returns - a defining attribute of randomness - we also can estimate that XME has a 56.5% probability of having a return greater than the expected 4-week return of a randomly selected stock. This in comparison to the 50% probability we would expect from a random stock.

Similarly, the 13-week expected return for XME is 7.2%, with a 60.8% probability of besting the base period expected return of 2.19%, and the 40-week expected return for XME is 21%, with a 64% probability of beating the base period expected return of 6.45%. All better probabilities for beating the returns of a randomly selected stock.

While even a 64% probability is better than a 50% probability implicit in a random selection, it’s still only a 64% probability. There is a 36% probability that it will underperform the expected return of a randomly selected stock. If you know anything about chance, you must know that a 36% chance of being wrong is more than enough to lose your shirt.

However, the Stock Trends Inference Model does tell us that XME is currently in a trend and momentum position that historically has exhibited tendency toward positive returns in the subsequent period. This gives us some confidence in making a directional trade, and can be used as the foundation of a derivatives trade (options) that further improves a trader’s probability of making a profitable trade.   

Stock Trends Slots Game

Stock Trends Slots

The stock market is a game of chance. Try your luck!

Stock Trends reports on weekly price and volume changes for thousands of individual North American stocks. Every eligible stock is assigned a series of Stock Trends indicators which interpret those changes. Match these indicators in the Stock Trends Slots game and learn how the changing market affects random outcomes presented by the game.

This game of chance is a great way to learn about the Stock Trends indicators and how they provide guidance toward probable outcomes.

Every week a new data set is created with the Stock Trends updated indicators. The Stock Trends Slots game data for the current week are the records that have Stock Trends indicator values for listed common stock, exchange traded funds, or income trust units on the following four exchanges - New York, Nasdaq, Amex, and Toronto.

How to Play

Player receives a set of 5 random draws to start the game.

On each draw or play, a random generator fills 5 rows with listings for 5 different stocks, with each record filling the columns in the order of stock symbol, Stock Trends trend indicator, Stock Trends volume indicator, Stock Trends RSI value, and Stock Trends RSI up/down indicator. Learn more about what these indicators mean in theLearn section of the Stock Trends website.

Each draw the player accumulates points and/or free plays with matching columns and rows, as described in the section below. Each week, with the changing market and the new set of Stock Trends indicators published, the probabilities and associated payouts change. See how the market trends affect the game play and how your luck ranks against other players!

At the end of each slots play players may choose to enter a Bonus feature play - the Stock Trends Investor Challenge! Enter your final portfolio of 5 stocks in the rolling 4-week Stock Trends Investor Challenge for a chance to win BONUS awards if your portfolio beats all challengers! Stock Market Investor Challenge winners are awarded every week. (Note: presently we are beta testing the game - no prizes are applied to winners)

Subscribers to Stock Trends Weekly Reporter have the option to lock rows before a spin and improve the odds of making another point scoring match. For instance, if a player has matched two rows, he can select those two rows to be locked in position such that in the following spin only the other three rows are randomly selected. The points payout for matches of additional rows remains the same, but the probability of making those matches improves.

The following rules apply to the locking of rows:

1) once a row match is locked, no points for the locked match are scored on the subsequent spins. That is, there is no double counting of matches when the matches are locked.

2) if the player locks more than two rows, the free spin combinations do not receive free spins. There is a cost to locking more than two rows - the player cannot accumulate additional spins with the free spin matches.

Play to improve your odds and enter your portfolio of stocks 
in the Stock Trends Investor Challenge!

As a subscriber to Stock Trends Weekly Reporter you will have access to additional game features:

• lock game rows to reduce random outcomes and improve your odds of making a match!
• enter your own custom 5-stock portfolio in the Stock Trends Investor Challenge.

GO TO STOCKTRENDS.COM TO LEARN MORE AND PLAY!!

Are you a systematic investor?

To be a successful trader one should be part data scientist. Although there are some highly successful traders that hinge their plan on subjective analysis artforms, the road to long-term profits in active trading should be grounded in the laboratory of data. The simple reason for this: failure, as much as success, must be measured and understood because market outcomes are often inherently volatile and unpredictable. Scientific method allows us to test trading hypothesis, learn from mistakes, and quantify risk. Systematic traders understand that without the integrity of data science, they are simply ticker tape cowboys.

Having an analysis framework is an important departure point for the systematic investor. That framework could be fundamental / value analysis - translating measures of intrinsic value into trading signals. An example of this would be the Dogs of the Dow trading strategy. For market technicians core intrinsic value relationships are too complex to model completely. Instead, a technical analyst focuses on patterns of supply and demand for an investment instrument. Those patterns of subjective market valuations are revealed in the price and volume of every stock.

“It’s not good enough to be anecdotal or doctrinaire when it comes to trading.”

Market technicians believe in the market’s message. They construct price and volume charts to read the tea leaves, so to speak, about the future direction of a market price. But here’s where this backward-looking artform often fails: how can a technical analyst place any faith in the reading of these charts? It’s not good enough to be anecdotal or doctrinaire when it comes to trading. It’s not good enough to show a tidy chart that reveals, for example, a head and shoulders pattern, and assert a projection for future price movement if there is no data from which to develop a measure of confidence in the prognostication.

There should be some standard of evidence to support a particular chart reading. If there is no evidence, there’s no foundation for acceptance. A technical trader should quantify the probabilities of future outcomes. Data science allows the diligent systematic investor to develop a level of confidence in a market environment that is fundamentally uncertain. Risk must be quantified!

How does Stock Trends help us turn stock market data into actionable quantitative measures of confidence? First, the Stock Trends indicators are by definition categorical - they translate market price and volume data into factor variables, or independent variables. In a data science setting we can use these independent variables as inputs and measure a relevant outcome, or output. The significant outcome for investors, of course, is the future return. If a dependent relationship is established between the inputs and the output, the trader can measure a confidence level for a desired trading outcome. Let’s now look at each of the Stock Trends indicators and how they fit our Stock Trends Inference Model.

The Stock Trends trend categories are the result of a method of translating market price data (quantitative variables) into categorical variables. For instance, last week’s closing price of Apple (AAPL) was $126.60. The Stock Trends trend indicator categorizes that price by applying a framework for qualification and putting the current price into a long-term price context. Using 13-week and 40-week average prices as guideposts, the trend indicator - now Stock Trends Bullish () - gives us a factor variable for the $126.60 market price.

 

 

 

 

 

A base test, then, would be to measure how a market price performs when it is in this trend category. However, we would want a more granular categorization because within each trend category there are many ancillary variable qualifications. For instance, a Bullish trend category can be relatively new, or it can be quite entrenched.

That is why Stock Trends publishes trend counters. They give us a better understanding of the time frame of the trend category. In our Apple example we can see that the current Bullish trend category has been in place for 92-weeks, about twice the average length of a typical Bullish trend, and that the current strong Bullish indicator has been in place for 22-weeks. So now we can ask the following question: how have stocks performed when they have been in a Bullish trend category for about 92-weeks, and also in a strong Bullish indicator for the most recent 22-weeks?

But our granularity can be improved even more. We also recognize that within any trend there are varying levels of price momentum. Stocks rally and retreat. The Stock Trends Relative Strength Indicators provide us with a method for translating price performance into factor inputs. The 13-week RSI values are discrete variables that can be cut into bins of specific ranges of values. By qualifying each stock’s trend by its relative price momentum to the broad market we can now be more specific about the characteristics we are sampling. In the case of our Apple example, its 13-week RSI is 100. This indicates the stock is only performing at par with the S&P 500 over the past 13-weeks. Now we can sample for Bullish stocks that also share this condition.

The RSI +/- indicator is a binary signal of whether a stock has outperformed or underperformed the broad market in the past week. Again, this indicator can be used as another factor input. Apple underperformed the S&P 500 index last week, and therefore has a (-) indicator.

Finally, another factor variable that Stock Trends creates is derived from the weekly volume of shares traded. Three different factor levels characterize the weekly volume, so that we can differentiate stocks further by which level the trading volume fits. Last week Apple had neither high nor low volume of trading, so its volume can be characterised as normal.

With these composite factor variables, published in each Stock Trends Report, the Stock Trends Profile presents the results of the Stock Trends Inference Model. In the case of Apple, shown below, we can see that the current Stock Trends indicators are relatively positive: the future 4-week return of Apple has a 57% probability being higher than the expected mean random return of a stock, which is 0%. Remember, that a randomly chosen stock has a 50% chance of having a 4-week return greater than 0% (see The random outcome benchmark). AAPL has a 62.2% chance of besting the base mean 13-week random return, which is 2.19%, and a 56% probability of besting the mean 40-week random return (6.45%) .

 

 

These probabilities might not strike you as significantly positive. However, they do indicate that the trend and momentum conditions for AAPL are sufficiently supportive of a continued bullish stance for Apple investors. The analysis also tells us that AAPL is more appealing than stocks with lower return expectations. You can compare the returns expectations of industry stocks in the associated heatmap that ranks the expected future returns.

This is the analysis framework of Stock Trends: translating the weekly trading statistics of an issue into factor input variables. It is how we interpret these variables and their significance in predicting future price performance that makes Stock Trends a unique and effective data science application. The Stock Trends Inference Model statistically measures the change in stock price that follows from each market condition defined by the composite of the inputs of each Stock Trends indicator combination.

Stock Trends covers the North American stock market - thousands of issues every week are categorized by the Stock Trends indicators. Each of these observations since 1980 - now numbering over 9.2-million records - can be used as input variables in models that measure the subsequent price change in the categorized stock. We can ask the question: what kind of returns did a stock have after it was categorized by the Stock Trends indicators? Do stocks that have a Bullish trend indicator and high price momentum perform better, on average, than other stocks? Is there any statistical evidence that momentum trading is profitable? Does a Bullish Crossover offer a good trade entry signal? More broadly, does the data support many of the doctrinaire positions of technical analysis? The Stock Trends Inference Model attempts to answer these type of questions.

"Every technical analyst who presents a price chart as evidence of a buy signal must also present a distribution graph of the expected returns. If they don't, take their advice with a grain of salt."

Stock Trends analysis framework is simple, but specific. It looks at certain important aspects of technical analysis - trend and price momentum. Another analysis framework might be centered on other algorithms of price and volume, and on a different time frame. Every investor has to choose what analysis framework fits their own assumptions about the dependent relationships in the market. However, each analysis framework must be measureable. The litmus test of this measurement should be the the presentation of data, the display of returns distributions. Indeed, in my opinion every technical analyst who presents a price chart as evidence of a buy signal must also present a distribution graph of the expected returns. If they don’t, take their advice with a grain of salt. Your success as a systematic investor will reflect your diligence in making data science integral to your trading strategies.

Return expectations for Twitter $TWTR #notgood

There’s a new social media button: UnLike. Twitter’s stock (TWTR) might be the first click. It’s tumble last week erased much of the first quarter goodwill the market had buffed up, closing at $37.84 on Friday and leaving behind the previous $50 support level in splinters. With any market response of this profile there are hails of panic, as well as resolve. Does an investor see this correction as the beginning of an even nastier fall or an opportunity to take advantage of nervous Nellies?

Technical analysis is, by definition, the study of price and trading activity. It seeks to answer the basic question posed in any market - Do I buy, or do I sell? - by interpreting past market action and prognosticating about future market action. Sometimes the market characteristics of a particular stock (or any trading instrument) are not that distinguishable or distinguishing. And then there are stocks with market activity that is much more categorically defined. Hello, Twitter!

Stock Trends allows us to isolate market characteristics - and especially so when there is a selloff. The 25.5% drop of TWTR last week flushed out many investors, and the usually high volume of trading indicator tells us the scope of this sentiment change is substantial. When we see a change to a Stock Trends Weak Bullish indicator () on this kind of price and volume move the technical aspects of the stock are quite distinguishable.

TWTR’s Stock Trends Report shows a combination of indicators that make this event categorically interesting: the trend indicator is Weak Bullish (), with a minor trend counter of 1, and a major trend counter now at 6, an RSI of 95 - , and an unusually high volume indicator (). The market characteristic described by this Stock Trends indicator combination is of a stock that is relatively early in a Bullish trend but has tripped rather suddenly on significant bad market news. While the drop in price was substantial last week, TWTR is still only underperforming the S&P 500 by 5% measured over the past 13-weeks.

The Stock Trends Inference Model (STIM) analysis is designed to make a statistical evaluation of market conditions - especially those market conditions that are most clearly defined. The Stock Trends Report on TWTR is now a good example. What does the STIM analysis say now about this stock’s future price expectations? Remember that the STIM analysis samples 30-years of Stock Trends data looking for stocks with similar indicator combinations, measuring post-observation statistics of 4-week, 13-week, and 40-week returns. From the samples we infer population parameters of these returns and estimate the probability of the current stock (here TWTR) bettering the estimated future returns of a randomly selected stock.

Here is the current STIM analysis of TWTR:

What does this analysis tell us? First, we see that the short-term price expectations are relatively neutral, with the mean return expectations near the expected return of a randomly selected stock (0%). There is a 51% probability that the 4-week return of TWTR will be positive (greater than 0%, the expected return of a broad market randomly selected stock). Not much better than the 50% probability that you would see a positive 4-week return in a randomly selected stock.

However, the 13-week and 40-week expected returns of TWTR are much more concerning. The probability of TWTR having a 13-week return better than the expected 13-week return of a randomly selected stock (2.19%) is only 45.2%. Looking further out on the time horizon is even more bleak. The probability of TWTR having a 40-week return greater than the expected 40-week return of a randomly selected stock (6.45%) is just 28.8%. Remember, a randomly selected stock has a 50% probability of having a 40-week return greater than 6.45%.

The STIM analysis tell us that TWTR, as defined by the current Stock Trends indicator combination, has a significantly low probability of delivering positive returns over the intermediate time periods ahead.

Introducing the 'Map of Stock Trends'

The Stock Trends Inference Model is a quantitative approach to interpreting the categorical data that is the core value-added analysis presented here. The Stock Trends indicators are derived from base tenets of the market technician’s encyclopedia - a toolset designed to reduce a complex market dynamic to a categorical, and hierarchical framework. By evaluating the statistical significance of this framework we can apply meaningful algorithmic trading methods.

However, the first step is to understand the data and interpret the Stock Trends Inference Model results. Every week we sample 30-years of data to assign a probability for future returns on over 7,000 North American stocks. Using combinations of categorical data and making assumptions about the distribution of returns, we apply statistical inference methods to differentiate stocks (ETFs and income trusts, too) by the estimated returns in the coming periods (4-weeks, 13-weeks, and 40-weeks). You can see the result of that analysis in the Profile section of each Stock Trends Report.

I’ve already introduced the Stock Trends Inference Model in previous editorials. Subscribers to Stock Trends Weekly Reporter can interpret this information weekly, as well as review the reports on issues with the best expected returns. The Stock Trends ‘Select’ report, as well as the Top 4-wk/13-wk/40-wk returns expectations reports give users a new way to make the Stock Trends reports actionable.

However, these reports can be augmented by data visualizations. Graphical presentations of data are always useful in translating vast data points into more accessible interpretations. A good graph saves us time and points us in the right direction.

The Stock Trends Profile reports include heatmaps which help us compare returns expectations among industry group member stocks. Another useful display method for this data, especially when we want to broaden the use of the data hierarchy, is a treemap. A treemap is specifically designed for hierarchical data and is commonly used. A popular example in our equity analysis space is the Map of the Market.

Today I am introducing a treemap of the Stock Trends Inference Model - the Map of Stock Trends. It takes the data results from the weekly analysis, sorting 4-week and 13-week returns expectations by trend category.

In the treemaps displayed below large capitalization stocks (U.S. stocks with a market cap greater than $1-billion, Canadian stocks with market cap greater than $500-million) are grouped by Stock Trends indicator (Bullish , Weak Bullish , Bearish , Weak Bearish , Bullish Crossover , Bearish Crossover ). Each stock within these groups are visually differentiated in two ways: spatially by their relative probability of a return greater than the base 13-week mean random return (2.19%) , with larger cells (higher probabilities) sorted and displayed from the upper left quadrant and moving down to the lower right corner for the lower value. Secondly, the 4-week returns expectations are differentiated visually by color gradation, with darker green hues representing stocks with higher probabilities of exceeding the base average 4-week random return (0%) and darker red hues representing the stocks with the poorest probabiltity of a positive return in 4-weeks.

 

 

Dark green cells in the upper left of each trend category are stocks with the best statistical trend characteristics. Dark red cells in the lower right quadrant of each trend category are stocks with the worst statistical trend characteristics.

Below are the current Map of Stock Trends treemaps for the U.S. and Canadian stock markets. Each Stock Trends trend indicator category grouping is identified by the translucent indicators in the background of each box. In the future the treemap will be developed in an application that allows users to click on an individual cell and go directly to individual Stock Trends Reports, but for now the visualizations help direct us to the stocks with the most favourable current Stock Trends Reports.

 

U.S. stock exchanges - big cap stocks

Toronto Stock Exchange - big cap stocks

Industry return expectations

Wondering which U.S. sectors and industry groups are signalling the best opportunities for returns in the period ahead? The Stock Trends Inference Model presents a quantitative look at period returns for individual stocks, and from those return expectations the sector and industry group average return expectations can be measured.

Recall that the Stock Trends Inference Model estimates the returns expectations for a stock, ETF or income trust given its current Stock Trends indicators. It does this by sampling for similar combinations of Stock Trends indicators over the past 30-years and measures post-observation price performance. From these samples statistical inference methodology is applied to estimate population mean and standard deviation parameters.

Every week over 6,000 issues have a Stock Trends indicator combination that has a minimum of 50 similar combinations in the data history, and you can find the resultant probability analysis in the Profile tab of these individual Stock Trends Reports. For instance, the current Stock Trends Profile of Solar Capital Ltd. (SLRC) shows that the expected 4-week return will be 5.6% and that the probability of a return greater than the base 4-week return expectation (which is 0%) is 62%. Our base expectation is that a stock has a 50% chance of a positive return in a 4-week period, so SLRC has a better chance of performing well, and is the top Nasdaq ST-IM Select stock this week.

The current week reports on 6,261 listings that have ST-IM returns estimations for 4-week, 13-week, and 40-week periods ahead. Breaking down those listings by sector and industry group gives us a better understanding of market timing trade opportunities. The heatmaps below rank sectors and industry groups by mean relative expectations over the three different time periods.

U.S sectors - ranking of return(%) expectations

 

Currently, the top returns expectations are found in utilities, healthcare, and technology sectors. Conglomerates, Financials, and Industrial sectors have the worst returns expectations.

Each sector breaks down into industry groups. The following heatmap shows how the returns expectations for these groups rank.

U.S industry groups - ranking of return(%) expectations

 

The industry groups with the best returns expectations, as averaged over the three periods, include utilities, consumer durables, and drug stocks. Financial services, conglomerates, and aerospace/defense stocks have the worst returns expectations.

The weekly Stock Trends ST-IM Select report shows the issues (stocks, ETFs, income units) with the best returns expectations over 13-weeks where the returns expectations are better than the base period returns expectations in all three periods (4-week, 13-week, and 40-week). [For rankings of return expectations within each period see the reports Top 4-week returns(%) expectations, Top 13-week returns(%) expectations, Top 40-week returns(%) expectations in the ST Filters reports section.]

Among the top ranked issues in the February 27th NYSE ST-IM report is the iShares U.S. Utilities ETF (IDU). Here Profile report shows that IDU has a 59% probability of beating the base period random return for each of the three periods. Recall that a stock chosen at random has a 50% chance of beating the broad market’s base period random return (i.e. a 0% return over 4-weeks, a 2.19% return over 13-weeks, and a 6.45% return over 40-weeks). With the given assumption of randomnessin market returns, a 59% probability of beating a random return constitutes an appreciable edge.

The heatmaps below rank the current returns expectations of large cap stocks represented in the Dow Jones Industrials index and the S&P/TSX 60 index. Microsoft (MSFT), Disney (DIS) and 3-M (MMM) top the DJI rankings, while Shaw Communications (SJR.B), Agnico Eagle Mines (AEM), and Blackberry (BB) have the best blue chip Canadian stocks return expectations. You can view the Profile report of each of these and all stocks on the Stock Trends Report page.

Dow Jones Industrials stocks - ranking of return(%) expectations

 

S&P/TSX 60 stocks - ranking of return(%) expectations

 

Bearish sentiment builds

Investors are always looking for the door. Even when returns are abundant and investor sentiment is wildly bullish, shareholders know that plump investment accounts are but paper profits - only real when the trigger is pulled and equity is once again cash. The degree to which investors look more nervously to the exit is proportional to the degree to which their equity positions are compromised. How we measure that compromise helps us identify critical shifts in investor sentiment and recognize high-risk market periods.

Stock Trends is by design a categorical reporting framework that gives us a measure of aggregate investor sentiment and a metric for determining when market participants are feeling the squeeze and most ready to dash for the cash. The Stock Trends Bull/Bear Ratio is now serving notice that the exit doors are wide open.

Most market analysts look at benchmark indexes of price level, pointing to areas of support and resistance to anticipate market rallies and corrections. Certainly, the 6% drop in the S&P 500 index from the market high in September sounded alarm bells. But we have had corrections of 5% and more multiple times during the bull market run since 2009. Can we expect this is just another typical and expected correction that will soon be subdued? Price level analysis can conjecture about that, but a measure of market breadth is the best barometer of how sentiment has truly shifted.

The Stock Trends Bull/Bear Ratio measures the distribution of Stock Trends trend categories and tells us something quite simple: are the majority of stocks trending positively or negatively? Are the diversified holdings of investors buoyed by a rising tide or sinking in aggregate?

The Stock Trends trend indicators categorize individual trends by the conditions of a simple moving average study. The base categories -Bullish or Bearish - are determined by the relationship of the 13-week and 40-week moving averages of price. If the 13-week average price is above the 40-week average price the stock is categorized as Bullish. If it is below the stock is categorized as Bearish. This is a factual reporting of past price performance.

The price smoothing aspect of average prices gives us a clearer idea of trends, and although these longer-term time parameters are lagging in nature, they do make it possible to characterize long-term price movement. It is this long-term price movement that most shifts the balance of investor sentiment and creates heightened periods of anxiety about equities.

Stock Trends tabulates the Bull/Bear Ratio for individual North American exchanges. The New York Stock Exchange Bull/Bear Ratio has been plummeting since August, and is now at 1.07. The Nasdaq Bull/Bear Ratio dropped below 1.0 in June and is now at 0.66. When we look at the composite of both major exchanges - some 5,660 common stocks that currently have Stock Trends trend indicators - we get a good look at the trend breadth of the U.S. stock market.

The graph below highlights periods where the Stock Trends Bull/Bear Ratio for the combined Big Board and Nasdaq exchanges has been rated as 'Bullish'. These shaded areas tell us when investor sentiment provides more fertile ground for market rallies and rebounds. There will be times when the S&P 500 index rallies without broader market support , like in late 2006, but these can represent divergences between large cap and small cap performances. Generally, a strong bullish investor sentiment is characterized across the stock market. The Stock Trends Bull/Bear Ratio gives us that representation of market breadth.

Where are we at now? The U.S. market Bull/Bear Ratio has been flirting with a Bearish investor sentiment reading since the market top in the summer, and has now dropped to 0.7. Canadian investors sentiment has also dipped into Bearish territory - the Stock Trends TSX Bull/Bear Ratio fell below 1.0 this week (now at 0.85).

Investors should take note that this aggregate North American trend condition makes the market vulnerable to a crash as investors increasingly weigh in about making an exit. The S&P 500 index's 4.1% recovery last week may be heartening, but fading investor sentiment should keep investors on high alert.

Stock Trends RSI +/- pattern analysis

Stock Trends Reports new Profile tab now also includes a pattern analysis of the RSI +/- indicator. This analysis looks to answer questions about a stock's volatility in particular price trends and how weekly price movement provides an indication of probable outcomes for the coming week. The Stock Trends RSI +/- indicator is a simple binary marker of weekly price performance relative to the benchmark market index. If a stock (all North American trading issues and indexes covered by the Stock Trends analysis) outperforms the benchmark (the S&P 500 for U.S. stocks, the S&P/TSX Composite index for Canadian stocks) the stock is assigned a (+). If it underperforms, it is assigned a (-). This binary notation of price performance can be a useful framework for an event sample space and inference model. From this we can derive probabilities of certain outcomes and estimate one week returns (%). Binary events are always interesting. They provide a simple modeled sample space of possible outcomes. The most common example is the flipping of a coin. We know when we flip a fair coin that there is a 50% chance that the outcome will be heads, and an equal 50% chance the outcome will be tails. How does this kind of random event compare to the binary RSI +/- event? Indeed, there is no surprise when the Stock Trends data reveals that almost all stocks have a near-50% chance of turning up an RSI +/- on any given week. But that is for a sample space that includes all the data. For instance, for IBM the Stock Trends weekly data shows that of the 1,800 weeks covered, 49.5% of observations show an RSI (+) as the weekly indicator. Although some stocks like INTC show a 51.6% probability of a (+) over their history, the mean value across all stocks tends to 50%. A question that comes from this random-like event becomes quite apparent: how does this probability change under different market characteristics? For example, if a stock is in a Stock Trends Bullish trend, what is the probability of an RSI (+) indicator? We can also ask what is the probability we will see an RSI (+) in the upcoming week if the previous week was also a (+) while the stock is in a Bullish trend? Using the samples of the stock's data history that match certain patterns of market performance and underperformance we can also derive similar probability statements. Although this analysis operates under the assumption of randomness in market returns, we are looking at the pattern of past performance and estimate the probability of an outcome derived from the event sample space. In short, like a gambler looking for evidence of an 'unfair' coin that can be capitalized on, we are looking for evidence of a pattern that provides us with better probabilities of a desired outcome than the base probability - which is 50%. Introduced in last week's editorial, the Stock Trends Reports Profile section is the first element of the Stock Trends Inference Model - the implied population parameters and distribution of like Stock Trends indicator combinations. Also presented was a heatmap that ranks the estimated returns of stocks in an industry group. These elements of the inference model focus on homogeneous patterns across markets and estimates 4-week, 13-week, and 40-week returns for individual stocks. The RSI +/- pattern analysis differs by focusing on patterns with the stock itself, estimating returns based on these internal samples. Last week AAPL was presented as an example, so we'll use it again for illustrating the RSI +/- pattern analysis. Below we can see the most recent history of the weekly Stock Trends indicators for AAPL. The current RSI +/- indicator is (-). In this analysis two categorical variables - the Stock Trends trend indicator and the RSI +/- indicator - are inputs. The output is the returns, or percentage change in price, in the week following the observation. What kind of returns (%) do the data show after the observation of a particular pattern of RSI +/- indicators when a stock is labeled in a specific trend? Here is the current RSI +/- pattern analysis of AAPL: To repeat, only weeks of the AAPL data showing the same trend indicator as the current trend indicator (strong Bullish) of AAPL are evaluated. Here we are looking to find how the binary RSI +/- probabilities differs from the probabilities we already understand about the aggregate for this and most stocks - a near 50% chance of either a (+) or a (-). Is the coin somehow biased in a particular trend? If so, to what degree? In this case, given the current RSI +/- patterns for AAPL, what does the data history tell us about how the stock performed subsequently to these patterns when the stock was in the same Bullish trend? The length of the longest pattern of RSI +/- indicators for each stock analyzed depends on the data available. Here the longest pattern measured is 6-weeks long. However, practical usage of the analysis probably lends itself best to periods of three or four weeks. In any event, the probabilities for binary outcomes as the pattern extends is of interest in evaluating the quality of the probabilities of the shorter term patterns. In the current AAPL example, the patterns all suggest that the current market underperformance indicated by the (-) will most probably be followed by a market outperformance (+). Of course, with a given probability of market outperformance we would like to know the returns expectations. If AAPL does outperform the market next week, what is the expected change in price in the coming week? The analysis above defines intervals for the returns expectations for AAPL for each length of the pattern - here from one to six weeks. This type of short-term price movement analysis can be used in tandem with the longer-term analysis provided by the Stock Trends Inference Model and detailed above the RSI +/- Pattern Analysis on the Profile tab of each Stock Trends Report. It can also be profitably used in short-term options trade setups, something Stock Trends will be able to advise about in the future.

The new Stock Trends Report Profile section

A much longer time in coming than originally planned, the new Stock Trends Report 'Profile' section is installed on the Stock Trends website. Available for most common stocks and exchange traded funds, the Profile report now features the Stock Trends Inference Model introduced in the past year. This analysis attempts to answer the very important question: what return expectations do the Stock Trends Reports imply? 

If you were lucky (?) enough to take statistics in your previous studies, you are probably reasonably versed in statistical inference methodology. You will know about measurements of central tendency and variability. You will know about the 'mean' and 'standard deviation' - both as descriptive statistics of a sample and estimated parameters of a population. And you will also know about sample spaces and probabilities. The Stock Trends Inference Model is an application of these basic statistical methods. 

 

If you were lucky enough to have avoided a statistics course in school, be assured this model can be explained in very simple and clear language. I've tried to do that in the editorials I have already written about this analysis, but let's summarize here. First, though, a description of methodology  should always be preceded by a statement of the research question and the biases of that question. 

 

Because the departure point for any model is the assumptions that underlie it, it's important to fully understand the fundamental premises of the Stock Trends Inference Model. The primary assumption is a core tenet of technical analysis - that price patterns repeat themselves. In order to illustrate this and display empirical observations of patterns market technicians must assert that these market price and volume patterns are homogeneous across markets.

  

What does that mean? It means that a price pattern observed in one market can be meaningfully applied to another market. A moving average crossover, for example, carries significance as much in AAPL as it does in ZNGA. A head-and-shoulders pattern found in the chart of IBM in 1980 a template for one in BAC in 2010 (please note: not factual dates for this example). 

 

If the application of technical patterns depends upon the premise that these patterns repeat themselves, what use is the observation of an historical pattern if it does not offer some predicative accuracy? It is not enough to be doctrinaire in our answer and provide anecdotal evidence of positive outcomes. We must provide a larger number of outcomes as evidence. 

 

Of course, no matter how large the sample size of the outcomes we present, the evidence will always be just a portion of the total number of possible outcomes across markets and across time. When we look at possible outcomes we must understand that these outcomes are not based on the market conditions of a particular moment. That would be unsatisfactory and biased. Because we cannot possibly know what will happen in any particular market, we must instead look at the estimating the character of all markets in a given condition. 

 

In the Stock Trends Inference Model the given condition is represented by the Stock Trends indicator combination. That combination is the aggregate of the Stock Trends trend indicator, the length of time the current trend category (BULLISH or BEARISH), the length of time of the current trend indicator, the 13-week Relative Strength (RSI) indicator value, the 1-week RSI +/- indicator, and the volume indicator. These indicators quantify and categorize a market condition in terms of trend and price momentum. Distinct combinations of these indicators qualify particular trends by price momentum and volume characteristics. 

 

If we look at the current Stock Trends indicator combination of AAPL, for example, we can see that this stock is in the 31st week of being labeled with a (strong) Bullish indicator and that it has been in a BULLISH trend category for 52-weeks. Its 13-week Relative Strength indicator (RSI) value is 109, indicating AAPL has outperformed the S&P 500 index by approximately 9% over the past 13-week period. The current RSI +/- indicator is (+) , indicating the stock outperformed the benchmark market index in the past week. Finally, there is no Unusual Volume indicator, indicating that last week's trading volume was not high or low enough to be assigned either a high or low volume indicator. 

 

 

 

 

Taken as a composite, these indicators tell us that AAPL is in a relatively solid long-term trend. Given these characteristics of a stock's trend and its length of trend, as well as its price momentum, what does this particular categorization imply about future price movement? 

 

Of course, we cannot precisely know what is to happen in the future. All we can do is look upon what has happened in the past and make some kind of estimation of what will happen in the future. Using statistical methods we can translate past observations of what has happened into a probability statement about what will happen in the future. The Stock Trends Inference Model attempts to do this. 

 

Below is the current Stock Trends Inference Model report found under the Profile tab of AAPL-Q. 

 

The first section shows the Sample distribution plot and estimated returns distribution for three different periods - 4-week, 13-week, and 40-week. In this case the sample - derived from the 30-year history of Stock Trends data - is 616 records of stocks which sported similar Stock Trends Report indicator combinations to the current indicator combination of AAPL. From this sample we are measuring the subsequent price performance over the three different periods. 

 

 

 

 

 

 

Here we ask of this sample: what kind of returns (%) did other stocks have which previously exhibited similar trend and momentum characteristics as defined by the Stock Trends indicator combination? 

 

The green density plot for each of the three periods is displayed. Each shows how the returns were distributed. This plot shows where most of the returns tended toward (central tendency) as well as the variability of the returns (variance). We are interested in measuring central tendency and variance of the sample because with those statistics we can estimate the average return and variance of the population of all returns associated with this Stock Trends indicator combination. Remember, the population of all returns is much large than this sample size - it includes returns not in this database. It includes future returns - the returns investors are most interested in! 

 

Using statistical inference methods we can estimate the mean of a population within a certain range, or interval, and we can be certain of that interval to a defined degree. Here our model is 95% certain of the mean intervals. Since we are most concerned about the lowest estimate of the interval, we know that there is only a 2.5% chance that the mean of the population is less than the low end of the interval. 

 

For the investor it is more meaningful to interpret the mean interval of the population as the estimated return of a portfolio of stocks that have the same Stock Trends indicator combination.  From this theoretical portfolio we can make another important assumption: that returns of randomly chosen samples, when estimated as the portfolio population, will have a normal, bell-shaped distribution. This assumption is an extension of a well-understood probability theory rule: the central limit theorem. 

 

This assumption - and evidence - of randomness in market returns provides us with a very useful framework for making probability statements about the expected return of a stock. With an estimated population mean, an estimated standard deviation of the distributions we can derive probability statements about observing a return above specific values from a normally distributed sample space. 

 

In short, the Stock Trends Inference Model translates our samples into an estimated return and gives us the probability that a return will better a given, benchmark return. 

 

What should that benchmark return be? It's not difficult to see that the base return we should measure against is the return of a randomly selected stock. If we are measuring returns based on the randomness of outcomes of a categorized sample (our Stock Trends indicator combinations), the base return should be the return we would expect if we randomly picked a stock across the broad market. Indeed, any trading system results should be measured against the results of a randomly selected portfolio.  If you can't beat the monkey, why bother? 

 

The base period random return benchmarks are as follows: 4-week (0%), 13-week (2.19%), and 40-week (6.45%). Each of these returns are the return means of over 500,000 samples taken at random over a 30-year period. Not surprisingly, the annualized return of randomly selected stocks is basically equivalent to long-term market returns - 8%. This sobering fact should remind market timing traders that no matter what analytical framework used, the returns generated by a buy-and-hold approach must be discounted, regardless of what the market actually provided during a particular period. 

 

 

I'll be looking at Stock Trends Inference Model analysis in the future, and pointing out ways to turn this analysis into profitable managed trades. Also, I'll be introducing an additional new analysis under the Profile section. It is a pattern recognition analysis that also employs statistical inference. Expect this content addition very soon.  

 

Another recent content addition to the Stock Trends Reports on the website is the charting application. This is a third-party application provided by Tradingview. For subscribers interested in marking up a chart of a given stock, Try it out! It also provides additional content including current intra-day pricing (15-minute delay), recent news headlines, social media comments from StockTwits, as well as technical and fundamental data.